This made the rounds last week: Substantiating Fears of Grade Inflation, Dean Says Median Grade at Harvard College Is A-, Most Common Grade Is A, from the Harvard Crimson.

Now, I agree that an A-minus is probably too high here. (Although Jordan Ellenberg says we shouldn’t worry about grade inflation.)

But does it really matter that the most common grade is an A? Consider, say, a situation where there is a “triangular” distribution of grades: 5 A, 4 B, 3 C, 2 D, and 1 F. The most common grade is an A, but the median is a B (and the mean is 2.67 on a 4.0 scale, a B-minus). If there are more grade categories the same thing happens – if we have a triangular distribution of grades such as this,  the median grade $1/\sqrt{2} \approx 0.71$ of the way up — about midway between a B-minus and a B on the 4.0 scale usual in the US. The mean grade would be $2/3 \approx 0.67$ of the way up the scale.  More generally, say grades are in the interval [0, 1].  If grades are beta-distributed with parameters 1 and $\beta > 1$ (my triangular idea is just the Beta(1, 2) distribution) then the modal grade will be 1 but the mean and median will be a good bit lower, $\beta/(\beta+1)$ and $2^(1/\beta)$ respectively.

(I’m not claiming that grades are beta-distributed, but that’s not a bad model for something that’s often thought of as being roughly normally distributed but has to be contained within an interval.)

Basically, modes don’t tell you much.

## 2 thoughts on “”

1. Tim says:

Exactly why it’s not of any particular interest that the most popular vehicle is the Ford F-Series.

2. JSE says:

Note that I didn’t write the headline for that article, which goes farther than the article itself does. Ten years later, I stand by what I wrote there, but would add that I _do_ think it’s a problem if grades are systematically awarded differently in different disciplines; it is bad if the decision whether to major in engineering in economics is affected by “I want to go to law school so need an A average so have to major in economics.”